This code only gives grids and not the steps and stars as in the test case I need to fix it:

from random import seed, randint

import sys

from collections import defaultdict

def display$\_$grid$()$:

for i in range$($len$($grid$))$:

print$(\text{'}\text{'},\text{'}\text{'}.$join$($str$($int$($grid$[$i$][$j$]!=0))$

for j in range$($len$($grid$))$

$)$

$)$

try:

arg$\_$for$\_$seed, density, dim $=($int$($x$)$ for x in

input$(\text{'}$Enter three positive integers: $\text{'}).$split$()$

$)$

if arg$\_$for$\_$seed $<mtext\; id="EditorElement\_268883"></mtext><mn\; id="EditorElement\_268884">0</mn>$ or density $<mtext\; id="EditorElement\_268898"></mtext><mn\; id="EditorElement\_268899">0</mn>$ or dim $<mtext\; id="EditorElement\_268909"></mtext><mn\; id="EditorElement\_268910">0</mn>$:

raise ValueError

except ValueError:

print$(\text{'}$Incorrect input, giving up$.\text{'})$

sys$.$exit$()$

seed$($arg$\_$for$\_$seed$)$

grid $=[[$randint$(0,$ density$)$ for $\_$ in range$($dim$)]$ for $\_$ in range$($dim$)]$

print$(\text{'}$Here is the grid that has been generated:$\text{'})$

display$\_$grid$()$

def stairs$\_$in$\_$grid$()$:

def is$\_$stair$($x$,$ y$,$ size, step$\_$size$)$:

$"""$Check if a stair with the given size and step size starts at $($x$,$ y$)."""$

if y $+$ step$\_$size $*($size $-1)>=$ len$($grid$)$ or x $+$ step$\_$size $*($size $-1)>=$ len$($grid$)$:

return False

# Check horizontal steps

for i in range$($size$)$:

for j in range$($step$\_$size$)$:

if grid$[$x $+$ i $*$ step$\_$size$][$y $+$ j$]!=1$:

return False

# Check vertical steps

for i in range$($size$)$:

for j in range$($step$\_$size$)$:

if grid$[$x $+$ j$][$y $+$ i $*$ step$\_$size$]!=1$:

return False

return True

stairs $=$ defaultdict$($lambda: defaultdict$($int$))$

dim $=$ len$($grid$)$

for step$\_$size in range$(2,$ dim $+1)$:

for size in range$(2,$ dim $//$ step$\_$size $+1)$:

for x in range$($dim$)$:

for y in range$($dim$)$:

if is$\_$stair$($x$,$ y$,$ size, step$\_$size$)$:

stairs$[$step$\_$size$][$size$]+=1$

# Convert defaultdict to regular dict for output

output $=\{\}$

for step$\_$size in sorted$($stairs$)$:

output$[$step$\_$size$]=[]$

for nb$\_$of$\_$steps in sorted$($stairs$[$step$\_$size$])$:

output$[$step$\_$size$].$append$(($nb$\_$of$\_$steps, stairs$[$step$\_$size$][$nb$\_$of$\_$steps$]))$

return output

# A dictionary whose keys are step sizes, and whose values are pairs

# of the form $($number$\_$of$\_$steps,

# number$\_$of$\_$stairs$\_$with$\_$that$\_$number$\_$of$\_$steps$\_$of$\_$that$\_$step$\_$size

# $),$

# ordered from smallest to largest number$\_$of$\_$steps.

stairs $=$ stairs$\_$in$\_$grid$()$

for step$\_$size in sorted$($stairs$)$:

print$($f$\text{'}$

For steps of size $\{$step$\_$size$\},$ we have:$\text{'})$

for nb$\_$of$\_$steps, nb$\_$of$\_$stairs in stairs$[$step$\_$size$]$:

stair$\_$or$\_$stairs $=$ 'stair' if nb$\_$of$\_$stairs $==1$ else 'stairs'

step$\_$or$\_$steps $=$ 'step' if nb$\_$of$\_$steps $==1$ else 'steps'

print$(\text{'}\text{'},$ nb$\_$of$\_$stairs, stair$\_$or$\_$stairs, 'with',

nb$\_$of$\_$steps, step$\_$or$\_$steps

$)$